animatable soft transition between sphere and cylinder
We can make use of Metaballs and Animation Nodes to achieve the desired effect.

The vertices of the mesh can be represented by a Ball Metaball, using such node tree:



We instance a Metaball Ball object, position it in place of the vertices and change its radius as we wish using an Object Attribute Output node and possibly its stiffness if you like.

Next, we can represent edges using Capsule Metaball, using such node tree:



We instance a Capsule Metaball, position it in the center of each edge, scale it using the size_x property based on the length of the edges using the Object Attribute Output node (We multiply it by 0.5 because capsule goes both ways), orient it along the edges using the Direction To Rotation node and control its stiffness and radius using Object Attribute Output node.

Which results:



Blend file for study:



Animating it and using non meshes structures is pretty easy in Animation Nodes. You may ask a question specific to exactly what you want to create. An example animation: